The angles of elevation of the highest point of a building from two points S and T are 60 degree and 30 degree respectively,T is vertically above S and ST=10m.Calculate the height of the building above the level of S
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To calculate the height of the building above the level of S, we can use the concept of trigonometry.
Let's consider triangle STP, where P is the highest point of the building.
We can break down triangle STP into two right-angled triangles: SPT and TPT.
In triangle SPT, the angle of elevation from point S is 60 degrees. We can use the tangent function to relate the height of the building (PT) to the distance from the building (SP).
tan(60 degrees) = PT / SP
Since the angle of elevation is given, we just need to find SP, which is the horizontal distance between S and P.
In triangle TPT, the angle of elevation from point T is 30 degrees. Again, we can use the tangent function to relate the height of the building (PT) to the distance from the building (TP).
tan(30 degrees) = PT / TP
Since the angle of elevation is given, we just need to find TP, which is simply the height of the building.
We are given that ST = 10m, which means TP = 10m.
Now, we can solve for PT in both equations and set them as equal.
From the first equation, we have:
PT = SP * tan(60 degrees)
From the second equation, we have:
PT = TP * tan(30 degrees)
Setting these equal to each other:
SP * tan(60 degrees) = TP * tan(30 degrees)
Since TP = 10m, we have:
SP * tan(60 degrees) = 10m * tan(30 degrees)
We can now solve for SP:
SP = (10m * tan(30 degrees)) / tan(60 degrees)
Using a calculator, we can find:
SP ≈ 5.77m
Finally, we can find the height of the building (PT):
PT = SP * tan(60 degrees)
Using the value of SP, we can calculate:
PT ≈ 5.77m * tan(60 degrees)
Using a calculator, we find:
PT ≈ 9.3m
Therefore, the height of the building above the level of S is approximately 9.3 meters.
Need answer
If the height of the building (above S) is h, and the distance from ST to the building is x, then we have
h/x = tan60°
(h-10)/x = tan 30°
Rearrange things a bit and you have
h cot30° = (h-10) cot60°
Now just solve for h.